Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-07-21
Class.Quant.Grav. 15 (1998) 143-152
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages, uses amsmath,amssymb, referees' suggestions implemented, to appear in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/15/1/010
The spatial gradient expansion of the generating functional was recently developed by Parry, Salopek, and Stewart to solve the Hamiltonian constraint in Einstein-Hamilton-Jacobi theory for gravitationally interacting dust and scalar fields. This expansion is used here to derive an order-by-order solution of the Hamiltonian constraint for gravitationally interacting electromagnetic and scalar fields. A conformal transformation and functional integral are used to derive the generating functional up to the terms fourth order in spatial gradients. The perturbations of a flat Friedmann-Robertson-Walker cosmology with a scalar field, up to second order in spatial gradients, are given. The application of this formalism is demonstrated in the specific example of an exponential potential.
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